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##1+x+x^2 = \dfrac{1-x^3}{1-x} = (1-x^3)\cdot \dfrac{1}{1-x} = (1-x^3)\sum_{k=0}^\infty x^k##.
Isn't this a contradiction since the LHS has degree ##2## while the RHS has infinite degree?
Isn't this a contradiction since the LHS has degree ##2## while the RHS has infinite degree?